PCSX2 is a great emulator that lets you play your ps2 games on your pc. Its simple to set up, is compatible with most games and lets you masivle improve the graphics (depending on your hardware)
Tou can find some detailed background at Wikipedia:
You will need the PCSX program, a bios from your ps2 system, the nuvee light gun plugin and a backup ISO of the game that you want to play.
How to install PCSX2 and the Nuvee light gun plugin:
Download the Nuvee light gun plugin to let you use your light gun:
Another good tutorial on getting PCSX2 set up:
Here is a video walking you through how to set up your lightgun with nuvee and pcsx2: